groups lists all groups a user belongs to, not all the other.

from man id:

By default, it prints the real user ID, real group ID, effective user
ID if different from the real user ID, effective group ID if different
from the real group ID, and supplemental group IDs.  In addition, if
SELinux is enabled and the 'POSIXLY_CORRECT' environment variable is not
set, then print 'context=C', where C is the security context.

groups lists all groups a user belongs to, not just all the others.

from man id:

By default, it prints the real user ID, real group ID, effective user
ID if different from the real user ID, effective group ID if different
from the real group ID, and supplemental group IDs.  In addition, if
SELinux is enabled and the 'POSIXLY_CORRECT' environment variable is not
set, then print 'context=C', where C is the security context.